TY - JOUR
T1 - Cyclically consecutive permutation avoidance
AU - Ehrenborg, Richard
N1 - Publisher Copyright:
Copyright © by SIAM.
PY - 2016
Y1 - 2016
N2 - We give an explicit formula for the number of permutations that cyclically avoid a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive 123-avoiding permutations in οn is given by n! times the convergent series Σ∞k=-∞ (3/2φ(k+1/3)n for n ≤ 2.
AB - We give an explicit formula for the number of permutations that cyclically avoid a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive 123-avoiding permutations in οn is given by n! times the convergent series Σ∞k=-∞ (3/2φ(k+1/3)n for n ≤ 2.
KW - Cyclic consecutive pattern avoidance
KW - Integral operators
KW - Spectrum
KW - Trace class operators
UR - http://www.scopus.com/inward/record.url?scp=84990982170&partnerID=8YFLogxK
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U2 - 10.1137/130946848
DO - 10.1137/130946848
M3 - Article
AN - SCOPUS:84990982170
SN - 0895-4801
VL - 30
SP - 1385
EP - 1390
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 3
ER -